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But then, in which case can it be musically correct to say "F-A# fourth"? It goes against rules.

The short version of this super long post:

* We should start a new thread, or continue this over PM's/email This is WAY offtopic, this should even be in a different forum!

* We are now discussing "spelling and grammar" in music

* Musical notation attempts to communicate what the composer wants.

* There are and have been different conventions, acceptable standards, customs... Those change with time and what is common at one point was/will be rubbish at some other. An example of this could be dots BEFORE notes to add one half of the value. We are used to see them AFTER the note, but the other version was used in the 18th century (Couperin, Rameau [you can even find them in his famous treatise]). Such a weird usage of dots indicated that the time should be taken from a note that would be found before the marked one (and not after, as we are used to see these days).

* There are no rules in music

* Notation is meant to make things easy, not hard. There are conventions in musical notation, not rules. And this conventions change with time.

* Conventions in notation are there for a reason. When conventions make no more sense, they are discarded.

I present a small silly example of non tonal music (ok, it is not music, but it still is an example), and also present enharmonic modulation in the 19th century as examples of why there is no need to stick to previous conventions when things can be made easier focusing on what is actually there (and not in what was usually there in previous styles and ideologies).

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I'll start by saying there are no rules in music. "Rules" have been a strategy used by teachers since antiquity: simple instructions for students to follow. Axioms are some times called rules, and axioms are required to create models of systems.

In music, we have organization. New ways to organize sound have come and gone. Some evolved and became new systems, some were not kept (for better or worse).

Music theory is created AFTER these systems have existed for some time. It is also possible to create a theoretical framework and then compose based on that (I guess this has been less common, and is usually nothing but a fad).

Music theory tries to identify patterns and structures in composers' techniques. Music theory has come with descriptions and models to understand and explain how music works.

There has never been anything stopping composers or musicians from doing whatever they want. Social constraints, conventions among peers, prejudice, the common denominator in taste, physical limitations, economic problems... those have an impact in the way musicians do their thing, but there's nothing stopping anybody from doing anything.

The famous treatises do not contain hard rules written in stone, they offer suggestions, examples and do their best to explain how things work. They come with some "rules of thumb" and clearly mention those are suggestions that will usually give good results. And that once the composer knows what he is doing, he is free to do as he pleases (as long as it yields the desired results). The actually want people to start from what is presented and go further ahead. They don't threat people with eternal suffering in a lake of fire. They have no reason to do that, and there's no way to punish the heretic.

Teachers create and "enforce" rules as a didactic strategy (there's evidence of that since antiquity, what we know as grammar originated from the way the latin teachers taught their students how to speak and write "proper" latin). Once people know what they are doing, they don't require rules. It becomes second nature, and we are able to see what is happening and what we want to do (obviously, if we are trying to write something in the style of Palestrina, parallel fifths are rubbish, but if we want something impressionistic, then it can work pretty well).

Now, I have a small example.

Our theoretical framework: assume we are going to write some music, using 12TET. This music is not tonal, and the main way to organize sound in this work is not "vertical". That is, we are not concerned with "chords" or vertical intervals, we want several independent parts to be played together and we are more concerned with the intervals between two adjacent notes in each independent part.

Why are we going to do that? Why not. Just because that's the idea we got, and it seems to be a good idea (just like Rameau thought it made sense to work with "chords" and not just intervals, or just like Schoenberg thought it could work to use series of 12 notes instead of major scales). This idea is not exactly new, either.

In that image, the same thing is written twice, but with different "spellings".

If we are not concerned with the vertical combinations (that is not the intent of this work), why should I write the last two notes of the first bar as Bb and F? Read one part at the time, they are easier to read without the extra natural signs (zero natural signs vs. 3 in each part).

In this example, it is trivial to read both versions, but what if things get more complicated? (complicated rythmic patterns, big jumps in each part and lots of notes everywhere).

My point is: What is more important? Writing things in an easy to read way, or trying to make this fit some model that has nothing to do with the intent of the music? This music is built of "horizontal parts", independent parts that are played together.

What if this music is composed using random numbers? If there happens to be a fifth at the end of that bar, it just happened, nobody wanted or was planning to have that fifth there. It is a byproduct. That's what the random numbers indicated, so that is what we write. How should we notate it? In the most complicated possible way? In the most readable manner?

I am writing in a horizontal way, writing rows of notes, and am not concerned with vertical matters.

You can say there is a fifth. Yes, both A#-F and Bb-F will be a fifth when played in 12TET (there can't be any difference). But I am not concerned with intervals, we can use the term fifth at some rehearsal just because it is a term that pretty much all musicians know (it is good to have names for things). But when I was writing this, I was not concerned with such a thing.

Is it correct to say that the distance between the last notes in both parts is a fifth (ignoring the octaves, of course)? Well, yes. When both notes are played, what we will hear is exactly what we call a fifth in 12TET. A#-F = Bb-F

Is there any reason to say those are not the same fifth in 12TET?

What's the point in saying it is a dimished sixth? What do we accomplish by doing that? Why should I say that's the proper name of this interval? In this context, intervals are not relevant to the structure of the music. The semantic content that was important for music in the common practice period is not relevant to this music.

So, why should I say this or that interval is not a fifth, or a fourth, or an augmented third? Same frequencies, and no semantic requirements to force us to use one name or the other.

If I were talking about maths, why should I say "it's the squared root of four" instead of saying "it's two"? If it is the same thing, I'd have to have a good reason to use the most complicated version. Well, what reason is there for me to do that in this musical example?

If we were concerned with chords and intervals, I'd go for Bb-F, if only because we are used to see a "fifth" spelled that way (it is a very very common thing to see). That would be a good reason. I agree It'd be easier to read, and I'd agree that writing Cbb-E# won't help anybody. That would make this thing harder to be read.

Of course, after doing that (writing Bb-F), I'd like to check the rest of each individual part to see if it is readable (or if I have a valid reason to write things in a specific different way).

Why don't I do both things? Why don't I try to keep Bb-F and get as few natural signs as possible. Well, why should I? If I have a very readable part, why should I do things differently? Isn't the intention of musical notation to communicate? Well, I am communicating what I want (I have no intentions in communicating something that was important for earlier music, but completely irrelevant for this).

In the theoretical framework for this example, just intonation doesn't exist (we are in 12TET). Chords and vertical intervals are not important (just because we don't want them to be), and the actual vertical combinations are pretty much byproducts of the main organization of the music (which is not tonal).

So I ask, what rules say that what I am doing here is wrong? Where can we find a list of those rules? Who created them, and why? Why are those rules relevant to this example?

The rules of tonal music? This is not tonal music.

Should we keep writing in a "traditional" way just to keep things being always the same? That is pretty much the opposite of what A LOT of composers from the late 19th century to our days did. Some were intentionally going against tradition, trying to make things different no matter what. Some were just finding new things because that's where they work took them, some were just lucky...

In any case, music changed, and the conventions changed. Just like language has evolved.

We could have used pianola rolls to write down this music, but this was written in western musical notation because it is a useful way to communicate music. This kind of notation is very common and we don't need to reinvent the wheel. Producing an easy to read score is a very good idea, specially knowing that things will get ugly.

We produced a readable score, that contains all the information we wanted it to have. We want musicians to be able to decipher this and create music.

If we are writing chords, we want them to be readable. If we are writing chromatic scales, we want them to look tidy and easy to follow... In this case, we are not concerned with enharmonics, because we are in ET.

What rules am I breaking?

Musical notation represents sound. It attempts to communicate something. The very same notation has been used in extremely different music (Schoenberg vs Monteverdi, early chants vs fake books), each with it's own semantics and organization.

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In the 19th century, we can find enharmonic modulations (think of Chopin's common Db major <---> C# minor). What once was a problem, became some kind of shortcut. (Db is NOT C#, or is it? It is the same note in a keyboard instrument with 12 notes per octave... that applies for many different tuning systems)

There are very few examples, if any, of music written in Db minor, the minor relative of Fb major (a scale that should have a key signature that includes one double flat).

Was Chopin (and all the other composers who did that) wrong? Was he breaking the rules of what is musically correct? Db is not C#, is it? Was he musically incorrect?

Can we find such a thing (Db as C#) in any music from the 16th century? Or from the 1600's?

Why did he used such an incorrect equivalence in his music?

Db minor would not be of much help communicating his intentions, C# minor works fine. Is it musically correct, or not?

In later composers:

If you see some of Schoenberg's dodecaphonic music, you can find C# next to Db. You can find the same chord "spelled" in different ways (some look weird, some look like normal triads). He was not after tonal chords.

If you see Ligeti's etudes (the devil staircase, for example), you can see chords and scales are written to be readable. Tritones are written in the most convenient way (augmented fourth and diminished fifths are irrelevant), chromatic scales are very easy to spot, all intervals are written to be easy to read.

If a composer is using quartal harmony, it helps to be able to see the fourths easily (yes, I accept tradition plays an important role).

If a composer wants independent musical lines, he concentrates on that. Augmented thirds or fourths... Sixths or fifths... If that is not relevant, the important stuff takes priority. This one might be uncommon, but what reasons are there to see this goes against some rules (what rules)?

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If the composer wants to add some extra meaning to a symbol, that is just fine. An example of this: explicit instructions saying that when a chromatic scale is written with sharps, it is meant to be cresc. and accel. and when it is written with flats, it is meant to be dim. and rall.

There could be some extra musical meaning: if an idea is written with sharps, then it is associated with X character (What do I mean by character? Think of Berlioz's Fantastic Symphony). If it is written with flats, it is associated with the other character, Y.

If any music is written with this in mind, and find that there is some F-A# interval, can we say it is not a fourth just because it's A# and not Bb? What about the other semantic content?

Can we say that is musically incorrect? Can we say that only the notation used by Mozart is correct? Mozart didn't have this in mind. And somebody composing in this manner will probably not have tonal conventions of the 18th century in mind.

The difference between intervals might not be part of the musical language, but the extra musical content represented by the A# is important.

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Does it sound like I am just making up crazy reasons to say F-A# is a fourth? Even crazier things were done in the 20th century.

There is a convention called "tuner sharps" whereby all accidentals are notated with sharps.That's all there is to it.

Of course if you look at for example 18th century fingering charts for the transverse flute or recorder, you'll see different fingerings for the sharps and flats, reflecting the common meantone tuning at the time.

Certainly, the "tuner sharps" convention explains why it is used in piano tuning just by looking at its name. Any information on when and how that convention started that would be very welcome.

We usually think of scales as a series of notes "going up". The convention for the Greeks was for notes to go down. If we go up, flats require too many natural signs. Maybe that's why the "tuner sharps" convention was adopted. Or maybe it was a decision based on simple practical, typographical reasons.

You can use whatever name you want for your notes, and write them as you want, sharps or flats, mostly if your score will be more readable of course. But there are definitions for the names of intervals: unison, second, third, etc...

And these definitions are not changed, nor affected by the intentions of composers when making music.

In musical terms, to say that F-A# is a fourth is an error. It goes against the definitions of the intervals. Fourths cover 4 notes and F-A# covers only 3: F, G and A so it's a third.

In math of course you can speak of square root of 4, or simply put 2. That will depend on what you want to express. But you can't say that square root of 4 is an irrational number and that 2 is a rational. The set of rational numbers is well defined and its definition won't change because of the way you use to express a number.

In the score you used as an example you can of course write Bb-F or A#-F as you wish, and it will be the same music. But if you write Bb-F you refer to it as a perfect fifth, and if you write A#-F then you speak of a diminished sixth, by definition. It is a matter of congruence, you can´t write it one way and spell it the other way.

What we piano tuners do of using only sharps and talk about intervals without respect of their definitions is a convention acceptable only because we are not musicians and we are not talking about or making music.

But take for example the book of Owen Jorgensen "Tuning", an exhaustive work about piano tuning from seventeenth century to our days, more than 700 pages long, with hundrets of temperaments explained. And he always respects the definitions of intervals, using flats as well as sharps where needed and respecting the musical definitions.

I think we tuners, using only sharps, are ignoring more than the definitions of intervals. We ignore musical theory and hystorical development of tuning practices and techniques.

In my course of piano technology, I was taught only one temperament: Equal.

If you look at Jorgensen's book, you'll see that ET was known from the beginning but needed centuries of evolution to be correctly tuned by ear.

I my opinion we should learn to tune pianos following this evolution. Beginning with Pitahgorean tunings, pure intervals, meantone temperaments, regular and irregular temperaments, circulating and non circulating temperaments, well temperaments and finally Equal Temperament.

It is unacceptable that professional tuners don't know the definitions of intervals!

Another example is this:

How many of us, pro's piano tuners, know the difference between a tuning and a temperament?

I think piano tuning is not only a craft but a science and we must study not only tune.

Some tuners are just looking for an easy job with some "artistic" attached to it.

Not all are understanding music, not understanding piano playing techniques, unfortunately.

To be honest, the best rebuilders and some technicians here are by evidence coming from the wood trade, and have limited understanding of the musical theory.

Hopefully there are many also that understand music, some of them have even learned to play at an almost professional level.

But when I see the mistakes done in regulation, in tuning, or in repairs, I understand that the problem is more in the schooling and the fine training.

For instance 8 times on 10 when I am asked for voicing, the badly bedded keyframe is what cause the primal source of discomfort. Then some tech voice the hammers to death with no result, the tone stay hard in some places.

or leads are used to "lighten" the touch, etc , etc..

Professional of the profession. Foo Foo specialistI wish to add some kind and sensitive phrase but nothing comes to mind.!

What I am understanding is: you consider a set of immutable and universal definitions to be rigidly applicable in all contexts and systems.

That is wonderful for physical principles but we are discussing symbols, nomenclatures, semantics and conventions in art. A single fixed point of view for ALL music leads to anachronistic affirmations.

Originally Posted by Gadzar

But take for example the book of Owen Jorgensen "Tuning", an exhaustive work about piano tuning from seventeenth century to our days, more than 700 pages long, with hundrets of temperaments explained. And he always respects the definitions of intervals, using flats as well as sharps where needed and respecting the musical definitions.

I think we tuners, using only sharps, are ignoring more than the definitions of intervals. We ignore musical theory and hystorical development of tuning practices and techniques.

In my course of piano technology, I was taught only one temperament: Equal.

If you look at Jorgensen's book, you'll see that ET was known from the beginning but needed centuries of evolution to be correctly tuned by ear.

I my opinion we should learn to tune pianos following this evolution. Beginning with Pitahgorean tunings, pure intervals, meantone temperaments, regular and irregular temperaments, circulating and non circulating temperaments, well temperaments and finally Equal Temperament.

For what Professor Jorgensen was working with, the conventions you have mentioned apply. But that doesn't mean they apply for everything. Also, his work was focused on tuning theory and practice, not on musical theory.

Not all music played or composed on ET is equal, talking about ET doesn't mean talking about all the different compositional systems that use that scale, or talking about all music that is played this days on a piano tuned in ET.

I (as a non-tuner) agree with you in that it can be great for tuners to be in contact with the history of tuning. I don't know if it is really indispensable, but I do think it is a worthwhile pursuit.

To all interested in this subject, please see my response today to the "HTTB - "Harmony Tuning" the Treble and Bass" thread today. I really hit upon some good technique last week while taking several days to tune entirely by ear.